通胀服从均值回复过程的最优消费和投资决策

Decision making for optimal consumption and portfolio under inflation with mean-reverting process

研究投资者在通胀环境下带递归效用的最优消费和投资问题.对投资者的通胀过程和财富过程进行描述,并用递归效用函数刻画投资者的偏好.利用动态规划原理,在跨期替代弹性为1时,考虑带通胀的最优消费和投资问题,建立相应的HJB方程,并根据假设的效用函数,推导出最优消费和投资的精确解.在跨期替代弹性不为1时,运用一阶近似,求出一般情形下最优消费和投资策略的近似解.最后,在给定模型参数下,分析通胀参数对消费财富比的影响.

This paper studies the optimal consumption and portfolio with the recursive utility under inflation. It describes an inflation process and investor＇s wealth process, and the investor＇s preferences with recursive utility. By using the principle of dynamic programming it builds the HJB equation of the optimal consumption and portfolio under inflation with unit elasticity of intertemporal substitution, and derives an exact solution. The policy of the optimal consumption and portfolio in a general case is derived through using first order approximation. Finally, the effect of the inflation parameters on the investor＇s decisions is analyzed.